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SSC CGL 2021 PYQ — Question 53

SSC CGL - 17 Aug 2021 - Shift 3 • Quantitative Aptitude • Q53

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The value of 2tan(60°−θ)tan(30°+θ)sin2(45°−θ)+cos2(45°−θ)\frac{\sqrt2 tan(60 ° - \theta)tan(30° + \theta)}{sin^2(45° - \theta)+ cos^2(45° - \theta)} is:

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Correct answer: A

Explanation

The correct answer is Option 1 i.e​​​​ 2\sqrt 2.

Here it is given that,

⇒ 2tan(60°−θ)tan(30°+θ)sin2(45°−θ)+cos2(45°−θ)\frac{\sqrt2 tan(60 ° - \theta)tan(30° + \theta)}{sin^2(45° - \theta)+ cos^2(45° - \theta)}

⇒ 2cot(90−60°+θ)tan(30°+θ)sin2(45°−θ)+cos2(45°−θ)\frac{\sqrt2 cot(90 - 60 ° + \theta)tan(30° + \theta)}{sin^2(45° - \theta)+ cos^2(45° - \theta)}

⇒ 2cot(30°+θ)tan(30°+θ)1\frac{\sqrt2 cot(30 ° + \theta)tan(30° + \theta)}{1} = 2\sqrt2